Cops and Robbers on [math]-Free Graphs

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-02-26 DOI:10.1137/23m1549912

Maria Chudnovsky, Sergey Norin, Paul D. Seymour, Jérémie Turcotte

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 1, Page 845-856, March 2024.
Abstract. We prove that every connected [math]-free graph has cop number at most two, solving a conjecture of Sivaraman. In order to do so, we first prove that every connected [math]-free graph [math] with independence number at least three contains a three-vertex induced path with vertices [math] in order, such that every neighbor of [math] is also adjacent to one of [math].

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无[数学]图形上的警察与强盗

SIAM 离散数学杂志》，第 38 卷，第 1 期，第 845-856 页，2024 年 3 月。摘要。我们证明了每一个连通的无[数学]图的 cop 数最多只有两个，从而解决了 Sivaraman 的一个猜想。为此，我们首先证明，每一个独立数至少为三的连通无[math]图[math]都包含一条顶点[math]按顺序排列的三顶点诱导路径，使得[math]的每一个邻接点都与[math]的一个邻接点相邻。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.